Currently, seismic measurements are most commonly made using geophones, which are rugged and work well at reasonable signal-to-noise ratios (SNRs) at higher frequencies, but have limited performance at low frequencies and lower SNRs. Digital microelectromechanical system (MEMS) sensors are also used, which have a wide bandwidth response, but a significantly higher noise floor compared to a geophone, and hence reduced sensitivity to small signals. Seismometers may also be employed, but are typically much more delicate, are more difficult to emplace, and are much more expensive (e.g., approximately $15,000 for a seismometer versus approximately $50-$100 for a geophone).
Seismic Sensor Overview
The most common seismic sensors use a proof mass suspended by a spring relative to a surrounding structure. New sensors using a fiber Bragg grating technique to measure ground motion are also becoming available, but are focused primarily on borehole type measurements. However, electromechanical systems remain the most prevalent. The entire assembly is placed in the ground, and as the Earth moves, the structure will move relative to the mass. The purpose of the sensor is to measure this relative motion between the mass and the structure, and from this measurement, deduce the motion of the Earth. As stated earlier, the motion levels can be very small (on the order of 10s of nanometers in some cases), the velocities are very small (typical units of nm/s), and the frequencies are low (down to well below 1 Hz).
The motion may be measured by measuring the relative displacement, velocity, or acceleration of the proof mass. Every sensor of this type has a resonant frequency, ω0=√{square root over (k/m)}, where k is the spring constant and m the proof mass. This determines several properties of the sensors of interest. The sensor response is given by the transfer function (impulse response) for a damped harmonic oscillator, which may be expressed in terms of displacement, velocity, or acceleration.
Intuitively, if the ground motion is sinusoidal at some frequency co, then the position x, velocity v, and acceleration a are given byx=cos(ωt)  (1)v=ω cos(ωt)  (2)a=ω2 cos(ωt)  (3)
Thus, for a large ω, a system measuring acceleration should be the most sensitive, but at low frequencies, velocity and acceleration sensitivity decrease quickly relative to a displacement measurement.
A geophone uses an inductive technique, namely, a coil surrounding a magnetic proof mass, and operates much like an audio speaker. As the coil moves relative to the magnet, from Faraday's law,
                    V        =                                            -              N                        ⁢                                          d                ⁢                                                                  ⁢                Φ                            dt                                =                                    -              N                        ⁢                                          d                ⁢                                                                  ⁢                Φ                            dx                        ⁢                          dx              dt                                                          (        4        )            
Where N is the number of turns. Hence, the sensor produces a voltage V that is proportional to the mass velocity.
Geophones work well and at relatively low cost, but have several fundamental limitations. One is noise, which will be discussed in the next section. Another relates to the transfer function. The mechanical sensitivity to acceleration is relatively constant below the resonant frequency. However, the electrical sensitivity decreases rapidly below the resonant frequency. Intuitively, low frequencies will result in low velocities, and hence, low voltages, which combines with increased noise at low frequencies to produce low sensitivity at low frequencies.
To overcome this limitation, a capacitive sensor is typically used. The mass motion changes the separation distance between two plates of a capacitor. By using the capacitor as a filter for an alternating current (AC) signal, the resulting signal envelope provides a measure of the capacitance. Hence, this type of capacitive sensor measures displacement instead of velocity. The system is highly nonlinear since the value of capacitance is inversely proportional to the distance between the plates, and a feedback loop is typically used to minimize the nonlinearities, provide higher dynamic range (to keep the plates from running into each other), and to improve noise performance. A commercial off-the-shelf (COTS) geophone has been modified by adding a capacitive sensing element to improve low frequency response and compared performance to a high-end capacitive seismometer, while a digital technique has also been demonstrated to improve low frequency sensitivity.
Intuitively, above the resonant frequency, the spring appears “soft,” such that the mass/spring system reacts slowly to rapid changes in relative position. Below the resonant frequency, the spring appears “stiff,” such that slow Earth motion results in very small changes in relative position. Thus, a system with a high resonant frequency will only detect accelerations at low frequency. This is the approach taken by a MEMS sensor. Although the sensor is capacitive with a feedback mechanism, the resonant frequency is very high, and the MEMS sensor is fundamentally an accelerometer. MEMS devices are generally rugged and compact and have a flat response over a wide bandwidth, but have a much higher noise floor, and hence, reduced sensitivity.
Noise and Sensitivity Limits
All of the traditional techniques have a fundamental problem in that they must measure an extremely small signal at very low frequencies, which must be done using inherently noisy and bandwidth-dependent amplifiers. Moreover, the sensing mechanisms themselves are inherently noisy due to kT noise generated within the mechanisms. The noise floor becomes particularly acute at low frequencies, as described below.
The two main sources of noise in seismic sensors are kT (or Johnson) noise and 1/f noise. kT noise is caused by random thermal fluctuations in electronic components, and increases with temperature. kT noise is present in the sensing coils and capacitors in the above designs, and gets worse as the coil and capacitor size increases. kT noise is also the primary noise source in amplifiers. kT noise is uniform in frequency space, and is zero mean.
Because the displacements/velocities/accelerations are so small, the resulting voltages that are generated are tiny, and control of thermal noise becomes critical. Most sensors attempt to control noise so that in some frequency range, it is lower than the Earth background noise. However, the noise typically becomes larger outside of that band.
Far more pernicious, however, is 1/f noise. 1/f noise is correlated such that it is not zero-mean. In other words, it will not average to zero. 1/f noise manifests itself in electronics as a slow drift, and becomes large at lower frequencies—much larger than the kT noise floor. For common seismic sensors, with tiny signals, 1/f noise is the dominant limiting factor at low frequencies.
All of the above techniques measure the motion (displacement, velocity, or acceleration) of a proof mass via tiny voltage fluctuations in either an inductive or capacitive sensing element. This inherently results in a difficult measurement problem due to the very small displacements (on the order of 10s to 1000s of nanometers), velocities (nm/s), and frequencies (0.1 to 0.001 Hz) of interest. Accordingly, an improved seismometer that is lower cost and able to measure very small displacements, velocities, and frequencies may be beneficial.